【作者】 何亮；

【导师】 任同群；

【作者基本信息】 大连理工大学 ， 微机电工程， 2015， 硕士

【摘要】 结构状态发生改变时,其动态特性会发生一定程度的变化,进而会在结构的振动响应中表现出来,基于振动分析的状态检测是结构状态检测中最常用到的方法。在工程实际中,结构可能存在着所受激励复杂多变、内部存在温度力、工况恶劣、损伤微弱等一系列问题,这些都增加了基于振动分析的结构状态的检测难度。本文以“高铁钢轨动静态综合实验平台”为实验对象,将四元数理论应用到振动信号分析中,把振动信号分析扩展到三个通道进行,以四元数傅立叶变换、四元数卷积、四元数矩阵奇异值分解、四元数旋转、K-L变换等理论作为主要的数学工具,辅以其它信号处理方法,如频谱分析、频响函数分析以及传递率函数分析等,对三通道振动信号处理中的若干问题进行了研究和探讨。本文主要研究工作及成果如下：(1)利用四元数奇异值分解进行信号去噪处理,通过仿真信号验证了该去噪方法的有效性。(2)在四元数及四元数傅里叶变换理论的基础上,构造了四元数振动响应信号,分别以仿真和实测钢轨振动信号为例,进行三通道振动信号频谱分析,并与传统单通道信号谱分析进行了对比,分析结果表明：利用四元数理论对三个通道信号整体进行频谱分析,融合了三个方向的信号,准确获得三个方向信号的全部频域信息。(3)利用四元数理论以及传递率函数的定义构造了四元数传递率函数,并对四元数传递率函数进行了探讨。单点激励时,传递率函数与激励的性质无关,是频响函数的函数,激励在四元数传递率函数的计算中不参与运算,只提供激振能量,传递率函数由激励的位置以及结构本身特性确定,这在损伤检测中具有重要意义。(4)在实验平台上采用钢轨扣件松脱模拟轨道结构状态变化,利用锤击法对钢轨施加激励,利用两个三轴传感器采集响应信号,计算得到四元数传递率幅频谱函数,利用K-L变换提取了不同轨道结构状态下四元数传递率幅值谱的特征向量,并分别构造数据库样本和测试样本,进行状态识别,多次实验识别成功率均在95%以上。(5)利用四元数运算描述空间旋转,对两个三轴传感器在不同安装姿态情况下的四元数传递率函数进行分析,证明了固定采样点情况下的四元数传递率幅值函数与传感器安装姿态无关。更多还原

【Abstract】 When structure state changes, the structural dynamic characteristics will change in a certain extent, these changes will be reflected in the vibration response. Under natural conditions, the complicated excitation, longitudinal temperature force, complicated operation conditions and weak damage will make the state identification based on vibration analysis more difficult. In this paper, the "high-speed rail experiment platform" was used as the research object and the quaternion theory was applied to the three channels vibration analysis.We discussed and studied the several problems in three-channel vibration signal processing with quaternion Fourier transform, quaternion convolution, quaternion matrix singular value decomposition, K-L transformation, quaternion rotation theory and other signal processing method, such as spectrum analysis, analysis of frequency response functions analysis and transmissibility functions, etc. The main work is as follows:(1) Verified the availability of the denoising method by quaternion singular value decomposition theory through the simulation signal.(2) Constructed the quaternion vibration response signal based on the quaternion theory and make the three-channel vibration signal spectrum analysis of the simulated and measured vibration signal of the rail, and then make a comparison with the traditional single channel signal spectrum analysis. The analysis results show that three-channel vibration signal spectrum analysis based on the quaternion theory could contain all three channels frequency domain information.(3) Constructed and studied the transmissibility functions based on the quaternion theory. It was proved that excitation only provide energy in situation of single point driven, it doesn’t participate in the calculation of transmissibility function. The transmissibility function is a function of frequency response function (FRF). It is determined by the location of the excitation and the characteristics of the structure itself, which is of great significance in the state detection.(4) Simulated different rail states by loosing different rail fastener one by one. The rail was excited by hammer and the response signals were acquired using two three axis sensor. The amplitude spectrum of quaternion transmissibility function was calculated, based on which the database sample and test sample were constructed. And then the state recognition experiment was carried out using K-L transformation to get the feature vector and a satisfactory result was also achieved. (5) Two three axis sensors are fixed in the same installation position but with different installation orientation. Then the quaternion transmissibility function was analyzed. It was proved that the quaternion transmissibility between two fixed sampling points has nothing to do with the direction of the sensors.更多还原